How Crank Climate Theories Work

A couple days ago, someone on social media shared with me one of their favorite crank theories about why the greenhouse effect isn't real using data from a couple planetary bodies. The person is not well-known, and who the person is doesn't really matter, so I'm not going to mention the name. I'm not so much interested in refuting this person here as I am in showing the thought processes that went into making the crank theory. It was a very good illustration of how crank theories come to be and how pseudoscience works. Here's a screenshot of the post:

So this person (we'll call him/her "J") multiplied planetary outgoing longwave radiation (OLR) by the molar mass of the atmosphere (M) for Venus and Earth and came up with the same number. The thinking here is that because OLR·M came up with the identical value for two planets, the temperature of planets must depend on the molar mass of the atmosphere, not the greenhouse effect. Even before considering the logic of this claim, a few things will become apparent to the astute viewer:

1. J got the units of his M values wrong. The numbers would have the units kg/mol, not g/mol.
2. J used the molar mass of dry air on Earth, but Earth's atmosphere contains water vapor. Since the molar mass of H₂O is only 0.018 kg/mol, the average M on Earth will be slightly less than the number J used.
3. J's OLR values had only two significant digits, but the product OLR·M agreed to 4 significant digits, suggesting that these numbers were deliberately chosen to produce the "same" result.
4. OLR (~240 W/m²) is essentially difference between upward surface emission (on Earth ~390 W/m²) and the greenhouse effect (on Earth ~150 W/m²), so this calculation assumes that the greenhouse effect is valid.

Already we can see that J is being sloppy, and clearly J is choosing numbers in order produce a result, not using the best empirical data. Let's help J out and do the math with correct numbers. On Earth, albedo is currently about 0.287, meaning that ASR is 1361·(1-0.287)/4 = 242.6 W/m². Earth's EEI is currently 1.42 W/m², so OLR is ~241.2 W/m². If we include water vapor for Earth, the molar mass of air is between 0.0285 and 0.02897. To be generous, since the troposphere averages ~0.46% water vapor, we'll scale J's value by that percent and the molecular weight of H₂O, which gives us a value of 0.02892 kg/mol. The units of OLR·M would be W·kg/m²·mol, which simplify to kg²/s³·mol. So with these corrections:

Earth: OLR·M = 241.2·0.02892 = 6.976 kg²/s³·mol

Now on to Venus. OLR on Venus in the range 160 and 162 W/m², so let's use 161 W/m². Using this and 0.04345 kg/mol we get

Venus: OLR·M = 161·0.04345 = 6.995 kg²/s³·mol

After correcting the empirical values, these numbers are only similar, not identical to four significant digits. But is that similarity just a coincidence? Well, let's try it for Mars (where M is similar to Venus) and Titan (where M is similar to Earth) to find out:

Mars: OLR·M = 111.7·0.04334 = 4.84 kg²/s³·mol

Titan: OLR·M = 2.38·0.0286 = 0.0681 kg²/s³·mol

We could go on to different rocky planets and moons with an atmosphere to test this further, but the fact is that there is no physical mechanism that would require any planetary body's total thermal emission to scale inversely with the molar mass of its atmosphere. OLR is determined by surface temperature and the greenhouse effect, and molar mass is determined by its chemical composition. If Earth's atmosphere was comprised entirely of O2 molecules, its molar mass would be 0.032 kg/mol. If it were comprised entirely of N2 molecules, it would be 0.028 kg/mol. Since both are transparent to outgoing longwave radiation, Earth's surface temperature would stay at its effective temperature with either atmosphere. At equilibrium with an albedo of 0.287, OLR would equal ASR = 1361·(1-0.287)/4 = 242.6 W/m² in both cases, but OLR·M would be different. Likewise, Titan is so far away from the Sun that it's very cold, and so Titan's OLR much smaller than Earth's, but the molar mass of Titan's atmosphere is similar to Earth's, so OLR·M for Titan is much smaller than OLR·M for Earth.

So what has J done? I think with a little speculation, we can get a pretty good idea. There's no reason why anyone knowledgeable about physics would think that multiplying OLR·M would yield something meaningful, so I strongly suspect J is just looking at tables of empirical values for planetary data and doing random calculations with the numbers to see if he can find results that agree. When he got numbers that were close for Venus and Earth, he massaged the data a little to make them agree to 4 significant digits. This appears to be how he found out that OLR·M on Venus and Earth produced the "same" results. He then had to ignore the fact doing the same calculation for Mars would show this to be just a coincidence. He then posted his crank theory on social media with a high degree of arrogance and sarcasm, perhaps hoping that people would confuse his confidence with competence. At no point does J attempt to explain why only a fraction of Earth's surface emission escapes to space, which is what J needs to do in order to show that the scientific understanding of the greenhouse effect is deficient in some way.

It occurred to me that this is exactly how a lot of pseudoscience and crank theories work, especially from the likes of Ned Nikolov and Robert Ian Holmes. Both follow this kind of pattern. For instance, Holmes found that that using this calculation T1 = ∜rTSI·T2 he could correctly "predict" Earth's temperature. Given Venus' 1-bar temperature (which was inaccurate in his paper) and the ratio of Earth's and Venus' TSI values, he got the correct result, and vice versa (more details here). He then conveniently ignored that this formula only works in the 3 specific cases that he included in his paper. The results were entirely coincidental, so Holmes had to cherry pick the results that "worked" and hide the ones that didn't. The crank theory methodology appears to be this:

1. Data Dredging. Do a bunch of random calculations from empirical data and see if you can find some similarities.
2. Data Massaging. When you find similarities, massage the numbers a little to get them to agree more precisely.
3. Cherry Picking. Ignore any and all similar calculations that would prove these results are coincidental.
4. Physical Illiteracy. Ignore the fact that these calculations are artificially contrived and make no sense of physics.
5. Spamming. Promote this on social media (or in predatory journals) as if you've uncovered evidence that 200 years of climate science has been wrong.
6. False Confidence. Add in some arrogant language to help readers confuse your confidence with competence, since any reader who checks up on you will find out that these are just coincidences.

I'm sure there are some crank theories that are developed differently, but the ones that appear on social media about climate (especially those that depend on planetary data) appear to work in this way. There are a lot of empirical values available for planetary bodies, and there are lots of potential calculations you can try to use to find agreements. These are fertile grounds for data dredging. You're bound to find similarities if you take the data dredging approach without considering physics. Then it's just a matter of coming up with an alternative "theory" and using whatever tactics possible to make sure no one actually checks up on you.